On normal numbers and self-similar measures

2021/07/06 by Baker, Simon
#Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2107.02699

Abstract

In this paper we prove that if \φ_i(x)=λx+t_i\ is an equicontractive iterated function system and b is a positive integer satisfying (log b)/(log |λ|)∉ℚ, then almost every x is normal in base b for any non-atomic self-similar measure of \φ_i\.

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